Answer:
[tex]f(x)-g(x)=\frac{-1}{4}x^{4}-3x^{3}[/tex]
Step-by-step explanation:
This is a subtraction between polynomials, since both functions are polynomials, hence, to solve the problem with need to perform the subtraction, by coefficients.
[tex]f(x)= \frac{1}{2}x^{4}+0x^{3}-x^{2}\\\\g(x)=\frac{3}{4}x^{4}+3x^{3}-x^{2}[/tex]
By performing the subtraction, we have:
[tex]f(x)-g(x)=\frac{-1}{4}x^{4}-3x^{3}[/tex]
